an:01973075
Zbl 1035.90053
Schultz, R??diger
Stochastic programming with integer variables
EN
Math. Program. 97, No. 1-2 (B), 285-309 (2003).
00097777
2003
j
90C15 90C11 90C06 90C57
Summary: Including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design. Starting from mean-risk approaches with different risk measures we identify corresponding two- and multi-stage stochastic integer programs that are large-scale block-structured mixed-integer linear programs if the underlying probability distributions are discrete. We highlight the role of mixed-integer value functions for structure and stability of stochastic integer programs. When applied to the block structures in stochastic integer programming, well known algorithmic principles such as branch-and-bound, Lagrangian relaxation, or cutting plane methods open up new directions of research. We review existing results in the field and indicate departure points for their extension.